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A225960
Number of permutations of [n] having exactly one strong fixed block.
3
0, 1, 1, 3, 9, 38, 198, 1229, 8819, 71825, 654985, 6615932, 73357572, 886078937, 11583028581, 162939646239, 2454350815033, 39415438078466, 672282146765650, 12137067564016917, 231223273420524311, 4635720862911035149, 97565878042828417209, 2150797149322137710488
OFFSET
0,4
COMMENTS
See A186373 for the definition of strong fixed blocks.
LINKS
Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..450 (first 201 and last 2 terms from Alois P. Heinz)
FORMULA
a(n) = Sum_{1<=i<=j<=n} A052186(i-1) * A052186(n-j).
a(n) = Sum_{i=0..n-1} A052186(i) * Sum_{j=0..n-i-1} A052186(j).
a(n) ~ 2 * (n-1)! * (1 - 1/n + 2/n^3 + 11/n^4 + 97/n^5 + 1105/n^6 + 13905/n^7 + 189633/n^8 + 2803873/n^9 + 44875599/n^10), for coefficients see A260957. - Vaclav Kotesovec, Aug 29 2014, extended Aug 05 2015
MAPLE
b:= proc(n) b(n):= -`if`(n<0, 1, add(b(n-i-1)*i!, i=0..n)) end:
a:= n-> add(b(i)*add(b(j), j=0..n-i-1), i=0..n-1):
seq(a(n), n=0..25);
MATHEMATICA
nmax = 25; A052186zero = Rest[CoefficientList[Assuming[Element[x, Reals], Series[-1/(ExpIntegralEi[1/x]/E^(1/x) + 1), {x, 0, nmax+1}]], x]]; suma = ConstantArray[0, nmax+1]; s = 0; Do[s = s + A052186zero[[j+1]]; suma[[j+1]] = s, {j, 0, nmax}]; Flatten[{0, Table[Sum[A052186zero[[i+1]]*suma[[n-i]], {i, 0, n-1}], {n, 1, nmax}]}] (* Vaclav Kotesovec, Aug 05 2015, more efficient program for big nmax *)
CROSSREFS
Column k=1 of A186373.
Sequence in context: A030869 A030846 A030818 * A020121 A270593 A059804
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 22 2013
STATUS
approved